Authors: Benjamin Qi, Andi Qu
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Focus Problem – read through this problem before continuing!
Instead of focusing on the pillars that should be destroyed, let's instead focus on the pillars that remain.
The total cost consists of the cost due to height differences plus the cost of destroying unused pillars. The latter cost is equal to the cost to destroy all pillars minus the cost to destroy the remaining pillars.
Since the cost to destroy all pillars is constant, we can thus turn the problem into one about building pillars instead of destroying them!
From this, we get a basic DP recurrence. Let be the minimum cost to build the bridge so that the last build pillar is pillar .
and the following recurrence holds:
effectively describes a linear function , where , , and
This means that we can use CHT to compute efficiently!
However, since is not monotonic, we can't use linear CHT using a deque, so we must settle with .
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